Question

Solve the following system of equations: 3x − 2y = 6 6x − 4y = 12

Answer 1

6x - 4y = 12...divide everything by 2
3x - 2y = 6

u notice it is the same as ur other equation...this means the lines are coincident...they are the same line and therefore, have infinite solutions.

Answer 2

Answer:

The system will have infinite many solution.

Step-by-step explanation:

Given system of equations: 3x − 2y = 6  and 6x − 4y = 12

We have to solve for the system of equation.

Consider the given system of equations:

3x − 2y = 6  ...............(1)

6x − 4y = 12 ..............(2)

Consider equation (2) ,

6x − 4y = 12

Divide equation by 2, we get,

3x - 2y = 6

Which is same as equation (1) ,

Thus, the system will have infinite many solution.

For a system of equation having infinite solution following condition holds:

$\frac{a_1}{a_2}=\frac{b_1}{b_2}= \frac{c_1}{c_2}$

 here, $a_1=3 , b_1=-2,c_1=6\\\\a_2=6 , b_2=-4,c_2=12$

Thus, we get,

$\frac{3}{6}=\frac{-2}{-4}= \frac{6}{12}=\frac{1}{2}$

Thus, the system will have infinite many solution.